Weeds ... stop getting in to my garden !!!!

In my backyard I put in some metal stripping and divided my yard from
the garden, but a bunch or grass and weeds crept in there from my
neighbors yard.
I had some asian jasmine ground cover as well and now there is a bunch
of grass (burmuda) in there.
I am peeved about having to re-do it again.
Here is what I am thinking:
1) I guess I have to build a barrier all the way around it and I guess
12" deep so the grass doesn't come in again.
2) I'm thinking that after I dig out my area I'll have to pour the
barrier with cement and make it continuous so grass can not weave its
way back in.
3) I'm thinking that all my jasmine and all my other plants are infused
with grass and it would be a waste of time trying to replant them or
save them.
Anyone been here before and have any advise?
Mike

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